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Multi-messenger constraints on the Hubble constant through combination of gravitational waves, gamma-ray bursts and kilonovae from neutron star mergers

The simultaneous detection of gravitational waves and light from the binary neutron star merger GW170817 led to independent measurements of distance and redshift, providing a direct estimate of the Hubble constant $H_0$ that does not rely on a cosmic distance ladder nor assumes a specific cosmological model. By using gravitational waves as ''standard sirens'', this approach holds promise to arbitrate the existing tension between the $H_0$ value inferred from the cosmic microwave background and those obtained from local measurements. However, the known degeneracy in the gravitational-wave analysis between distance and inclination of the source lead to a $H_0$ value from GW170817 that was not precise enough to resolve the existing tension. In this review, we summarize recent works exploiting the viewing-angle dependence of the electromagnetic signal, namely the associated short gamma-ray burst and kilonova, to constrain the system inclination and improve on $H_0$. We outline the key ingredients of the different methods, summarize the results obtained in the aftermath of GW170817 and discuss the possible systematics introduced by each of these methods.